Symplectic Constrained Dynamics Integrators

I4)-(4.I6) symplectic (in the sense outlined above for holonomic systems)  

It is difficult to make sense of this question, since (4.14)-(4.16) does not even constitute a map of the co-tangent bundle. On the other hand it is not too difficult to correct this defect by incorporating an additional projection onto the cotangent space  

The demonstration that the method is symplectic can be seen as a consequence of 

Thus we may apply Lemma 4.1 with y replaced by each g, to demonstrate 

Using similar argumentation based on the properties of the wedge product, we next show 

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